A firm prediction of the cold dark matter model of cosmological structure formation is that the Milky Way should host a huge population of self-bound dark matter subhalos. The vast majority of these subhalos are likely devoid of stars, but a tiny minority are expected to host the luminous dwarf galaxies observed around the Milky Way. These are the most dark matter-dominated galaxies presently known, and are therefore excellent laboratories for testing theories about galaxy formation and the properties of dark matter. I will show that the Milky Way's satellite galaxies appear to have substantially less dark matter than is predicted by numerical simulations. Explaining this deficit requires a Milky Way that is atypical in multiple respects, extreme galaxy formation feedback, or non-standard dark matter physics. I will discuss these intriguing possibilities and some resulting implications.